Abstract
Extensive turbulence measurements from the Limagne and Beauce experiments were used to compute a characteristic time scale of the turbulence field (Τ = second moment/dissipation rate) for turbulent kinetic energy, temperature and humidity variances, and temperature-humidity covariance. The height variations of these time scales were analysed. The characteristic half-time scale Τ/2 of the turbulent velocity field was found, as expected, to be of the same order of magnitude as the large-eddy time scale Τ L = Zi/w*, showing that the turbulence structure is controlled by large eddies in the bulk of the mixed layer. The increase of Τ/2 above z/Z i ∼- 0.7 implies, however, that this time scale is no longer relevant to destruction of turbulent kinetic energy in the statically stable region with negative heat fluxes. An effective time scale Τeff, introduced by Zeman (1975), has been computed and its behaviour discussed.
The scales for θ′ 2, q′2, and θ′q′ were found to be much shorter than Τ. Furthermore, a significant difference in behaviour was also revealed between the characteristic time scales of temperature and humidity fields in the stable layer.
By using these experimental estimates, we tested some of the models for molecular dissipations, which are currently in use in higher order closure atmospheric boundary-layer models. The parameterized dissipation rates for θ′ 2, and q′ 2 agree well qualitatively with experimental estimates in the bulk of the mixed layer. In the stable layer, however, the parameterized dissipation rate ε θ tends to become larger than the experimental ones although the parameterized dissipation rate ε q still agrees with the experimental ones.
For the molecular dissipation of θ′q′, this current model becomes physically inconsistent in the middle part of the mixed layer, because this term may become a production term for temperature-humidity covariance.
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References
André, J. C.: 1976, ‘Une approche statistique de la turbulence inhomogène’, Thèse de Doctorat d'Etat, Université de Paris VI.
André, J. C. and Lacarrère, P.: 1975, ‘Les ondes de gravité internes et leur traitement numérique dans les modèles de la couche limite atmosphérique’, La Météorologie V, 33, 1–9.
André, J. C. and Lacarrère, P.: 1980, ‘Simulation numérique détaillée de la couche limite atmosphérique: comparaison avec la situation des 2 et 4 juillet 1977 à Voves’, La Météorologie VI, 22, 5–46.
André, J. C., De Moor, G., Lacarrère, P., Therry, G., and Du Vachat, R.: 1978, ‘Modeling the 24-hr Evolution of the Mean and Turbulent Structures of the Planetary Boundary Layer’, J. Atmos. Sci. 35, 1861–1883.
Blackadar, A. K.: 1962, ‘The Vertical Distribution of Wind and Turbulent Exchange in Neutral Atmosphere’, J. Geophys. Res. 67, 3095–3102.
Bolgiano, R.: 1962, ‘Structure of Turbulence in Stratified Media’, J. Geophys. Res. 67, 3015–3023.
Busch, N. E.: 1973, ‘On the Mechanics of Atmospheric Turbulence’, in D. H. Haugen (ed.), Workshop on Micrometeorology, American Meteorological Society, 1–61.
Coulman, C. E.: 1978, ‘Boundary Layer Evolution and Nocturnal Inversion Dispersal, Part II’, Boundary-Layer Meteorol. 14, 493–513.
Deardorff, J. W.: 1974a, ‘Three-Dimensional Numerical Study of the Height and Mean Structure of a Heated Planetary Boundary Layer’, Boundary-Layer Meteorol. 7, 81–106.
Deardorff, J. W.: 1974b, ‘Three-Dimensional Numerical Study of Turbulence in an Entraining Mixed Layer’, Boundary-Layer Meteorol. 7, 199–226.
Deardorff, J. W., Willis, G. E., and Lilly, D. K.: 1969, ‘Laboratory Investigation of Non-Steady Penetrative Convection’, J. Fluid Mech. 35, 7–31.
Deardorff, J. W., Willis, G. E., and Stockton, B. H.: 1980, ‘Laboratory Studies of the Entrainment zone of a convectively mixed layer’, J. Fluid Mech. (part I) 100, 41–64.
Gossard, E. E. and Hooke, W. H.: 1975, ‘Waves in the Atmosphere’, Developments in Atmospheric Science, Vol. 2, Elsevier, 456 pp.
Guillemet, B., Isaka, H., and Mascart, P.: 1983, ‘Molecular Dissipation of Turbulent Fluctuations in the Convective Mixed Layer, Part I: Height Variation of Dissipation Rate’, Boundary-Layer Meteorol. 27, 141–162.
Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Coté, O. R., Izumi, Y., Caughey, S. J., and Readings, C. J.: 1976, ‘Turbulence Structure in the Convective Boundary Layer’, J. Atmos. Sci. 33, 2152–2169.
Launder, B. E.: 1978, ‘Heat and Mass Transport’, in P. Bradshaw (ed.), Turbulence 2nd Edition, Springer-Verlag, pp. 231–287.
Lenschow, D. H., Wyngaard, J. C., and Pennell, W. T.: 1980, ‘Mean-Field and Second-Moment Budgets in a Baroclinic Convective Boundary Layer’, J. Atmos. Sci. 37, 1313–1326.
Louis, J. F., Weill, A., and Vidal-Madjar, D.: 1983, ‘Dissipation Length in Stable Layers’, Boundary-Layer Meteorol. 25, 229–243.
Lumley, J. L.: 1964, ‘The Spectrum of Nearly Inertial Turbulence in a Stably Stratified Fluid’, J. Atmos. Sci. 21, 99–102.
Lumley, J. L.: 1974, ‘Research Notes on the Buoyant Transport Model’, Ecole Centrale Lyonnaise, France.
Lumley, J. L. and Khajeh-Nouri, B.: 1974, ‘Computational Modeling of Turbulent Transport’, Adv. Geophys. 18-A, Academic Press, 169–192.
Mascart, P., Isaka, H., and Guillemet, B.: 1978, ‘Kelvin-Helmholtz Waves Observed by Aircraft at Different Stages of Their Life Cycle in a Low-Level Inversion’, Boundary-Layer Meteorol. 15, 31–35.
Mellor, G. L. and Yamada, T.: 1974, ‘A Hierarchy of Turbulence Closure Models for Planetary Boundary Layer’, J. Atmos. Sci. 31, 1791–1809.
Nicholls, S. and Readings, C. J.: 1979, ‘Aircraft Observations of the Structure of the Lower Boundary Layer over the Sea’, Quart. J. Roy. Meteorol. Soc. 105, 785–802.
Panofsky, H. A., Tennekes, H., Lenschow, D. H., and Wyngaard, J. C.: 1977, ‘The Characteristic Turbulent Velocity Components in the Surface Layer under Convective Conditions’, Boundary-Layer Meteorol. 11, 355–361.
Phillips, O. M.: 1967, ‘On the Bolgiano and Lumley-Shur Theories of the Buoyancy Subrange’, in A. M. Yaglom and W. I. Tatarsky (eds.), Atmospheric Turbulence and Radio Wave Propagation Nauka, 121–128.
Sommeria, G.: 1974, ‘Modèle tridimensionnel pour la simulation numérique de la couche limite planétaire — Application à la couche limite tropicale’, Thése de Doctorat d'Etat, Université de Paris VI, 100 pp.
Tennekes, H. and Lumley, J. L.: 1972, ‘A First Course in Turbulence’, MIT Press, 300 pp.
Townsend, A. A.: 1966, ‘Internal Waves Produced by an Convective Layer’, J. Fluid Mech. (Part 2) 24, 307–319.
Tuzet, A. and Isaka, H.: 1983, ‘An Experimental Investigation of Turbulence Structure in Convective Mixed Layer: An Interfacial Scaling of Entrainment-Induced Temperature and Humidity Fluctuations’, to be submitted to Boundary-Layer Meteorol.
Weinstock, J.: 1978, ‘On the Theory of Turbulence in the Buoyancy Subrange of Stably Stratified Flows’, J. Atmos. Sci. 35, 634–649.
Wyngaard, J. C. and Coté, O. R.: 1974, ‘The Evolution of a Convective Planetary Boundary Layer — A Higher Order Closure Model Study’, Boundary-Layer Meteorol. 7, 289–304.
Wyngaard, J. C., Coté, O. R., and Rao, K. S.: 1974, ‘Modeling the Atmospheric Boundary Layer’, Adv. Geophys. 18-A, Academic Press, pp. 193–211.
Wyngaard, J. C., Pennell, W. T., Lenschow, D. H., and Le Mone, M. A.: 1978, ‘The Temperature Humidity Covariance Budget in the Convective Boundary Layer’, J. Atmos. Sci. 35, 47–58.
Zeman, O.: 1975, ‘The Dynamics of Entrainment in the Planetary Boundary Layer: A Study in Turbulence Modeling and Parameterization’, Ph.D. Thesis, The Pennsylvania State University.
Zeman, O. and Lumley, J. L.: 1976, ‘Modeling Buoyancy Driven Mixed Layers’, J. Atmos. Sci. 33, 1974–1988.
Zeman, O. and Lumley, J. L.: 1979, ‘Buoyancy Effects in Entraining Turbulent Boundary Layers: A Second-Order Closure Study’, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (eds.), Turbulent Shear Flows I, Springer-Verlag, pp. 295–306.
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Isaka, H., Guillemet, B. Molecular dissipation of turbulent fluctuations in the convective mixed layer part II: Height variations of characteristic time scales and experimental test of molecular dissipation models. Boundary-Layer Meteorol 27, 257–279 (1983). https://doi.org/10.1007/BF00125001
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DOI: https://doi.org/10.1007/BF00125001